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" The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. B' ADC A' D' C' Hyp. In triangles ABC and A'B'C', ZA = ZA'. "
Plane Geometry - Page 180
by Arthur Schultze - 1901
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Second-year Mathematics for Secondary Schools, Volume 2

George William Myers - Mathematics - 1910 - 304 pages
...triangle having one angle 60. Apply the theorem — two triangles having an angle in each equal are to each other as the products of the sides including the equal angles (see 248, p. 231). 7. On a given base, construct a triangle equal to a given triangle not having...
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Plane Geometry: With Problems and Applications

Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Plane - 1910 - 304 pages
...triangles ACD and EBC that AC- BC= CE- CD. 430. EXERCISES. 1. The areas of two parallelograms having an angle of the one equal to an angle of the other are in the same ratio as the product of the sides including the equal angles. 2. Three semicircles of equal...
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Plane Geometry: With Problems and Applications

Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Plane - 1910 - 300 pages
...triangles ACD and EBC that AC- BC = CE- CD. 430. EXERCISES. 1. The areas of two parallelograms having an angle of the one equal to an angle of the other are in the same ratio as the product of the sides including the equal angles. 2. Three semicircles of equal...
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Wentworth's Plane Geometry

George Albert Wentworth, David Eugene Smith - Geometry, Plane - 1910 - 287 pages
...one are equal respectively to two angles of the other. PROPOSITION XIV. THEOREM 288. If two triangles have an angle of the one equal to an angle of the other, and the including sides proportional, they are similar. ABA B' Given the triangles ABC and A'B'C',...
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Elements of Plane Geometry

William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 286 pages
...respectively, to two angles of the other. PROPOSITION XVIII. THEOREM. 368. Two triangles are similar if they have an angle of the one equal to an angle of the other and the including sides proportional. EF Given As ABC and DBF in which XA = XD, and — = — . DE...
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Class Teaching and Management

William Estabrook Chancellor - Teaching - 1910 - 384 pages
...bases. 6. Find the locus of points equidistant from the three edges of a trihedral angle. 7. Prove: The areas of two triangles which have an angle of the one supplementary to an angle of the other are to each other as the products of the sides including the...
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The Teaching of Geometry

David Eugene Smith - Geometry - 1911 - 358 pages
...better suited to the use of pupils who may be working only with the tape, is given on page 99. THEOREM. The areas of two triangles which have an angle of...products of the sides including the equal angles. This proposition may be omitted as far as its use in plane geometry is concerned, for we can prove...
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Plane Geometry

Clara Avis Hart, Daniel D. Feldman - Geometry, Modern - 1911 - 328 pages
...other sides are each equal to s. PROPOSITION VIII. THEOREM 49R Two triangles which have an angle of one equal to an angle of the other are to each other...products of the sides including the equal angles. 4 GCD 2. 3. To prove Given A ABC and DEF, with Z A = Z D. A ABC AC-AB A DEF DF . OB ARGUMENT Let h...
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Cadet Life at West Point

Hugh T. Reed - 1911 - 330 pages
...extreme and mean ratio. Theorem : The areas of two triangles which have an angle of one equal to the angle of the other are to each other as the products of the sides including those angles. Problem : Given a circle of unit diameter and the side of a regular inscribed polygon,...
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Bulletin, Issues 1-11

Education - 1911 - 1030 pages
...line. GROUP II. 4. Prove that two tetrahedrons having a trihedral angle of one equal to a trihedral angle of the other, are to each other as the products of the edges including the equal trihedral angles. 5. Prove that the volume of a triangular pyramid is equal...
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